Morse theory and a scalar field equation on compact surfaces
By A. Malchiodi. Advances in Differential Equations, 2008
111 citations recorded by the source corpus.
he aim of this paper is to study a nonlinear scalar field equation on a surface Σ via a Morse-theoretical approach, based on some of the methods in [25]. Employing these ingredients, we derive an alternative and direct proof (plus a clear interpretation) of a degree formula obtained in [18], which used refined blow-up estimates from [34] and [17]. Related results are derived for the prescribed Q-curvature equation on four manifolds.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/fda28b9d6de7db2dfe2af8a9d01b520f2c79fc41
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Citations in the corpus
- Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, background): “(2) have been intensively studied by many mathematicians, for there are many applications in geometric and physical problems, for example, in the problem of prescribing Gaussian curvature [9,12, 8], in the theory of the mean field equation [16,17,10,11,19,32] and in the Chern–Simons theory [38, 41,1”
- Symmetric Joins and Weighted Barycenters (2006, background): “This has been obtained in the case of topological surfaces in [20].”
- Supercritical conformal metrics on surfaces with conical singularities (2011, methodology): “In particular, a flow defined by Malchiodi [36] allows us to adapt to Jλ the classical deformations lemmas [6, Lemma 3.”